With regard to a well-known engine brake running mode (fuel cut inertia running mode) performed with engine brake applied by driven rotation of an engine while a power transmission path between the engine and wheels is kept connected, an inertia running mode performed with an engine brake force made lower than that of the engine brake running mode is conceived for extending a running distance and contributing to improvement in fuel consumption. A device described in Patent Document 1 is an example thereof and a control device is described that performs, for example, a neutral inertia running mode performed with a power transmission path disconnected between an engine and wheels while the engine is put in idle operation, or a free-run inertia running mode performed with the power transmission path disconnected between the engine and the wheels while the engine is stopped, thereby eliminating the engine brake so as to extend a running distance and contribute to improvement in fuel consumption. Although not depicted in Patent Document 1, another known method of reducing an engine brake force to extend a running distance and contribute to improvement in fuel consumption is a cylinder resting inertia running mode performed by resting at least a part of cylinders of the engine while the power transmission path is kept connected between the engine and the wheels. Resting a part of the cylinders in this way reduces a pumping loss generated during driven rotation of pistons, resulting in a reduced engine brake force.